In many domains, learners extract recurring units from continuous sequences. For example, in unknown languages, fluent speech is perceived as a continuous signal. Learners need to extract the underlying words from this continuous signal and then memorize them. One prominent candidate mechanism is statistical learning, whereby learners track how predictive syllables (or other items) are of one another. Syllables within the same word predict each other better than syllables straddling word boundaries. But does statistical learning lead to memories of the underlying words--or just to pairwise associations among syllables? Electrophysiological results provide the strongest evidence for the memory view. Electrophysiological responses can be time-locked to statistical word boundaries (e.g., N400s) and show rhythmic activity with a periodicity of word durations. Here, I reproduce such results with a simple Hebbian network. When exposed to statistically structured syllable sequences (and when the underlying words are not excessively long), the network activation is rhythmic with the periodicity of a word duration and activation maxima on word-final syllables. This is because word-final syllables receive more excitation from earlier syllables with which they are associated than less predictable syllables that occur earlier in words. The network is also sensitive to information whose electrophysiological correlates were used to support the encoding of ordinal positions within words. Hebbian learning can thus explain rhythmic neural activity in statistical learning tasks without any memory representations of words. Learners might thus need to rely on cues beyond statistical associations to learn the words of their native language.